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Categorical and algebraic aspects of Martin-Löf Type Theory

✍ Scribed by Adam Obtułowicz

Publisher
Springer Netherlands
Year
1989
Tongue
English
Weight
939 KB
Volume
48
Category
Article
ISSN
0039-3215

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✦ Synopsis

In the paper there are introduced and discussed the concepts of an indexed category with quantifications and a higher level indexed category to present ~tn algebraic characterization of some version of Martin-L6f Type Theory. This characterization.is given by specifying an additional equational structure of those indexed categories which are models of Martin-L6f Type Theory. One can consider the presented characterization' as an essentially algebraic theory of categorical models of Martin-L6f Type Theory, The paper contains a construction of an indexed category with quantifications from terms and types of the language of Martin-L6f Type Theory given in the manner of Troelstra [11]. The paper contains also an inductive definition of a valuation of these terms and types in an indexed category with quantifications.

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